We develop and study two techniques for the calculation of threebody
scattering amplitudes. The first is a variational principle based on
the Faddeev equations. In form it resembles a Schwinger principle. The
wave functions that are varied are products of the two-body potentials and
the normal three-body wave function. This results in a very simple
asymptotic behavior, even for energies above the breakup threshold.
Numeric results are presented for s-wave calculations using separable
potentials for elastic, rearrangement and breakup scattering. The convergence
is rapid and the technique seems very successful. Accuracies on the order
of several parts per million are easily achieved. The specific forms of
the equations for problems involving two or three identical bosons are also
presented and the breakup calculations for these cases are presented as
Dalitz plots.
The second technique is based on the analytic structure in the total
energy of the three-body T-matrix. The T-matrix is computed for energies
less than the physically allowed energies and the results of these calculations
are then numerically analytically continued to the physical region.
Because the wave function has very simple asymptotic behavior beneath threshold,
these calculations are easy to do. Calculations have again been done
for separable potentials so the results can be compared with the results
from the first technique. We conclude that this is a reliable technique
for scattering beneath the breakup threshold and that useful results are
achieved for positive total energies, if there is not too much breakup
scattering. The technique is then applied to a local s-wave calculation
using Yukawa potentials. A Kohn type variational principle is used to
find the beneath threshold T-matrices. The final results show good convergence and with the above mentioned lUnitation, this appears to be a
good technique for local calculations.